A lattice is called isodual if it is geometrically congruent to its dual.
We show that the densest three-dimensional isodual lattice is the
``central centered-cuboidal'' lattice, a lattice which
is in a sense the mean of the face-centered and body-centered cubic lattices.
This lattice is also the most economical three-dimensional isodual covering.
We give a number of other dense isodual lattices in R^n, for n <= 24.
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